{% extends "homepage.html" %}

{% block content %}


    <h2> {{ KNOWL('artin.dimension', title='Dimension') }} </h2>
    <p> ${{ object.dimension() }}$ </p>

    <h2> {{ KNOWL('artin.conductor', title='Artin conductor') }} </h2>
    <p> ${{ object.conductor() }} $</p>

    <h2> {{ KNOWL('artin.number_field', title='Artin number field') }} </h2>
    <p> $\mathbb{Q}[x]/({{ object.number_field_galois_group().polynomial().latex()}})$ </p>
    
    <h2> Associated group action </h2>
    <h3> Abstract isomorphism type</h3>
    <p> {{ object.number_field_galois_group().G_name() }}, of size  ${{ object.number_field_galois_group().size() }}$.</p>
    
    <h3> Generators of the permutation group</h3>
    <center>
    <table class="ntdata">
        <thead>
          <tr><td>Positional notation</td><td>Cycle notation</td>
          </tr>
        </thead>
      <tbody>
        {% for gen in object.number_field_galois_group().G_gens()%}
        <tr> <td>${{gen}}$</td><td>${{gen.cycle_string()}}$</td></tr>
        {% endfor %}
      </tbody>
      </table>
    </center>
    </p>
    
    <h3> Conjugacy classes and associated representation</h3>
    <p> <center><table class="ntdata">
      <thead><tr><td>Index</td><td>Size</td><td>Order</td><td>Action on $r_1 \cdots r_{ {{object.number_field_galois_group().degree()}} }$</td><td>Action on $r_1 \cdots r_{ {{object.number_field_galois_group().degree()}} }$</td><td>Character value</td></tr></thead>

      <tbody>
        {% for gen in object.number_field_galois_group().conjugacy_classes()%}
            <tr {% if loop.index == object.number_field_galois_group().complex_conjugation()%}class="redhighlight"{%endif%}> <td>${{loop.index}}$</td><td>${{gen.size()}}$</td><td>${{gen.order()}}$</td><td>${{gen.representative()}}$</td><td>${{gen.representative().cycle_string()}}$</td><td>${{ object.character()[loop.index - 1] }}$ </td></tr>
        {% endfor %}
      </tbody>
      </table>
      </center>
       The red line marks the conjugacy class containing complex conjugation.
    </p>
        
{% endblock %}
